You can ask AT&T to unlock your phone, but they most likely will not do so until it is fully paid off.
Other than that, yes, it should work in Italy with a local SIM card and, yes, your data/contacts/etc. should survive the change.
Do not get yourself locked into an Italian carrier until you have tested it fully in whatever area you are settling, as coverage can vary significantly. Typically, Italians do not lock in anyway; you buy a SIM card for a one-time fee (somewhere around €25 or so) that comes with xx number of minutes plus yy MB data. Then, you simply top it off the way you would a prepaid credit card. You can go into most tabacchi and many other locations and purchase a "ricaricard"; it used to be that you would actually get a card with a code hidden under a scratch-off (like a lotto scartch off card), but you may just as likely receive a simple printed receipt with the code visible. You then send a text including that code to actually top off your account.
Generally speaking, if you eventually want to be able to download apps that are designed for the European/Italy market, you will have to register a "local" credit card (that is, one with an Italian billing address) to your Apple account. Otherwise you be locked into only apps/music and so on that are available in the US (I'm presuming here) market.